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2.4: Row Echelon Form (REF) matrices, Reduced Row Echelon Form (RREF) matrices and Elementary Row Operations. Elementary Row Operations (ERO) 3 basic operations performed on a system of linear equations or the augmented matrix obtained from the system, without changing the solution set. 1. Interchange ($) two rows of the augmented matrix: R $ R : i j Note: Your book uses Permute Row i and Row j, illustrated as P : ij 2. Replace (!) a row, say row i, of the augmented matrix by a nonzero multiple of itself aR ! R : i i Note: Your book uses Multiply each element of Row i by a nonzero constant a; illustrated as M (a): i 3. Replace a Row by a nonzero multiple of another Row plus itself aR + R ! i . j